23.6.14 problem 14

Internal problem ID [6813]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 6. THE EQUATION IS NONLINEAR AND OF ORDER GREATER THAN TWO, page 427
Problem number : 14
Date solved : Tuesday, September 30, 2025 at 03:52:17 PM
CAS classification : [[_3rd_order, _missing_x], [_3rd_order, _missing_y], [_3rd_order, _with_linear_symmetries], [_3rd_order, _reducible, _mu_y2], [_3rd_order, _reducible, _mu_poly_yn]]

\begin{align*} 2 y^{\prime } y^{\prime \prime \prime }&=2 {y^{\prime \prime }}^{2} \end{align*}

✓ Maple. Time used: 0.027 (sec). Leaf size: 20

ode:=2*diff(y(x),x)*diff(diff(diff(y(x),x),x),x) = 2*diff(diff(y(x),x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 \\ y &= \frac {{\mathrm e}^{c_1 \left (c_2 +x \right )}}{c_1}+c_3 \\ \end{align*}

✓ Mathematica. Time used: 0.345 (sec). Leaf size: 26

ode=2*D[y[x],x]*D[y[x],{x,3}] == 2*D[y[x],{x,2}]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_2 e^{c_1 x}}{c_1}+c_3\\ y(x)&\to \text {Indeterminate} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*Derivative(y(x), x)*Derivative(y(x), (x, 3)) - 2*Derivative(y(x), (x, 2))**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - Derivative(y(x), (x, 2))**2/Derivative(y(x